Probabilite bann seri dan roulet
Bann long seri enn mem koler kouran. Zot osi pa vedir nanye pou tour swivan.
Sink rouz swivan: 2.7%. Dis: 0.074%. Lor enn sesion 200 tour, enn seri sis enn mem koler paret pli souvan ki li pa paret.
Konbien souvan enn seri pert vini
Enn pari peman egal lor enn rou enn sel zero perdi 19 tour lor 37. Sakenn ranze montre sans ki enn seri tour donn tou perdi, ek konbien enn zwer Martingale, ki doub apre sakenn pert, inn perdi ziska la.
| pert youn deryer lot | sans | apepre 1 lor | perdi ziska ler | pari swivan |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Sans-la se 19/37 miltipliye par li-mem enn fwa par pert, konte depi enn tour donn. Enn long sesion ena boukou tour kot enn seri koumsa kapav koumanse, alor lor enn lasware li boukou pli probab ki seki enn ranze fer krwar.
Enn sel seri
ProbabilitematematikProbabiliteSans enn rezilta, depi 0 ziska 1 ouswa depi 0% ziska 100%. Enn nimero: 1/37 = 2.70%.Lir tou → ki k prosenn tour tou rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → se (18/37)ᵏ. De: 23.7%. Sink: 2.7%. Dis: 0.074%, apepre 1 lor 1,350. Ven: 1 lor 1.8 milyon. Ven-sis, rekor Monte Carlo: 1 lor 137 milyon. Sa bann-la se probabilite enn seri presi ki koumanse lor enn tour presi, ek se enn kestion ki preske personn pa vremem pe poze.
Dan enn sesion
Kestion ki dimounn vremem pe poze se “eski enn seri k pou paret enn kote dan mo sesion?”, ek repons-la boukou pli gran ki (18/37)ᵏ akoz enn sesion 200 tour ofer preske 200 plas kot enn seri kapav koumanse. Enn seri sis ouswa plis enn mem koler, rouz ouswa nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou →, paret dan enn sesion 200 tour apepre 94% dan ka; wit ouswa plis apepre 47%; dis ouswa plis apepre 14%. Si ou nom koler-la avan, sans-la bese, ziska apepre 75%, 27% ek 7%. Enn zwer ki asize enn aswar pou trouv long seri sak aswar.
Kifer Martingale bizin pran sa an kont
Sakenn progresionstrateziProgresionNenport ki regleman ki sanz miz-la dapre bann rezilta avan. Progresion negatif ogmant li apre pert, pozitif apre gin.Lir tou → negativ ena enn longer seri ki kas li: sis pert depi enn baz $10 avek enn limit $500, dis pou FibonaccistrateziFibonacciProgresion ki swiv sekans 1, 1, 2, 3, 5, 8, 13…: enn pa devan apre enn pert, de pa deryer apre enn gin.Lir tou →, sink pou tripl miz lor douzennpariDouzenn1–12, 13–24 ouswa 25–36, peye 2:1.Lir tou →. Probabilite enn seri sis pert lor peman egal se (19/37)⁶ ≈ 1.8% par tantativ, ek enn sesion 200 tour kontenir petet 100 tantativ, alor kasir-la arive dan apepre kat sesion lor sink ki ena sa longer-la. Probabilite bann seri dan roulet se rezon ki sa falez-la pa rar.
Nimero so ek nimero fre
Mem kalkil-la aplik pou pari lor enn sel nimeropariPari lor enn sel nimeroEnn sel nimero, peye 35:1.Lir tou →. Dan 300 tour, nonb atandi par nimero se 8.1; ekar-tipmatematikEkar-tipRasinn kare varyans; distans tipik ant enn rezilta ek valer atandi.Lir tou → apepre 2.8. Enn nimero pou sorti 15 fwa ek enn lot 2 fwa zis par azar, sak fwa. Enn tablo rezilta ki met an evidans nimero “so” pe met an evidans lao enn distribision normal. Laboratwar-la explike komie tour bizin avan ki enn nimero somitNimero soEnn nimero ki finn sorti pli souvan ki atandi dernieman. Lor enn rou zis li pa prevwar nanye.Lir tou → vedir kiksoz (plizir milye, lor enn sel rou idantifie).
Lindepandans, samem tou
Enn seri dis rouz pa fer nwar pli probab, ek li pa fer rouz pli probab non plis. Toulede se 18/37. Seri se enn propriete sekans aleatwar ek se zot absans ki ti pou sispe: enn sekans 200 tour san okenn seri pli long ki kat ti pou enn prev manipilasion boukou pli for ki enn sekans avek enn seri douz.
Formil
Kestion
26 nwar dan Monte Carlo 18 out 1913, samem sa enn fame-la. 32 rouz swivan ti raporte dan enn kazino amerikin an 1943. Toulede konpatib ar azar, kan ou pans komie tour bann kazino fer.
Li 18/37 dan tou ka. Parye seki ou plan dir, ouswa pa parye ditou.
Non. Enn defo paret kouma serten kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → ki sorti pli souvan lor plizir milye tour, pa kouma seri enn koler.
Lamizman ar matematik
Esey rezoud zot ou mem avan. Sakenn solision kase; ouver li kan ou pare.
Komie tour enn rou eropeen bizin, an mwayenn, avan ki sakenn 37 nimero finn sorti omwin enn fwa?
Montre solision-la
Repons Apepre 155 tour an mwayenn; medyann-la se 147.
Kont latant enn nouvo nimero a la fwa. Premie tour touzour montre enn nouvo nimero. Kan ou finn trouv 1 nimero, 36 kazekipmanKazEnn bann 37 konpartiman avek nimero lor rotor. Osi: slot, cup.Lir tou → lor 37 nouvo, alor prosin nouvo nimero pran 37/36 tour an mwayenn. Kan ou finn trouv k nimero, li pran 37/(37 − k).
Adisionn bann latant: 37/37 + 37/36 + 37/35 + … + 37/1 = 37 × (1 + 1/2 + 1/3 + … + 1/37) ≈ 37 × 4.20 = 155.5 tour.
Plipar sa latant-la se lafin. Dernie nimero tousel pran 37 tour an mwayenn, ek dernie sink apepre 85. Lor enn rou amerikin mem som-la donn apepre 161. Sa se problem kolekter koupon; mem mwayenn-la sorti depi kalkil standar.
Lor 37 tour enn rou eropeen, enn tour pou sakenn kaz, komie nimero diferan ou kapav atann pou trouve?
Montre solision-la
Repons Apepre 23.6. Apepre enn tier bann nimero, apepre 13, pa sorti ditou.
Pran enn nimero, kouma 17. Lor sakenn tour li pa sorti avek sans 36/37, alor li rat tou 37 tour avek sans (36/37)³⁷ ≈ 0.363.
Tou nimero ena mem sans, alor an mwayenn 37 × 0.363 ≈ 13.4 nimero manke ek 37 − 13.4 ≈ 23.6 sorti, boukou ladan de fwa ouswa plis.
Zwer roulet apel sa lalwa bann tier. Se pa enn lalwa, zis aritmetik bann repetision: dan enn seri ki osi long ki rou-la, apepre enn tier bann nimero res deor, lor enn rou zis kouma lor nimport ki lot. Lor 38 kaz sa par-la osi (37/38)³⁸ ≈ 0.363; pou enn gran rou li stabiliz pre 1/e ≈ 0.368.
Enn kamarad montre ou de lis 50 koler, rouzpariRouzPari peman egal lor 18 nimero rouz. An franse: rouge.Lir tou → ouswa nwarpariNwarPari peman egal lor 18 nimero nwar. An franse: noir.Lir tou →, ki dir ki sakenn sorti lor enn rou kot bann zerorouZeroSel kaz ver ki okenn pari peman egal, douzenn ouswa kolonn pa kouver; sours lavantaz kazino. Osi: enn sel zero, 0.Lir tou → finn retire. Enn sanz koler 25 fwa ek so pli long seri se sis. Lot-la sanz 35 fwa ek zame depas trwa. Lekel ki finn fabrike?
Montre solision-la
Repons Dezyem-la. Enn vre lis sanze apepre 24 ouswa 25 fwa. Enn lis ki sanz 35 fwa paret apepre enn fwa lor 500 lis, ek enn lis san okenn seri pli long ki trwa apepre de fwa lor 100.
Sakenn nouvo koler swa repet dernie-la swa sanze, mwatie-mwatie, alor 49 lokazion pou sanze donn 24.5 sanzman an mwayenn, plis ouswa mwins apepre 3.5. Trant-sink se trwa sa bann pa-la pli ot ki mwayenn-la; enn rou zis prodir otan sanzman-la apepre enn fwa lor 500 lis.
Bann seri rakont mem zistwar. Enn vre lis 50 ena enn seri kat ouswa plis apepre 98% di tan, ek so pli long seri pli souvan sink ouswa sis.
Dimounn ki bizin invant enn lis aleatwar sanze tro souvan, akoz enn seri kat ouswa sink paret zot kouma enn model. Taylor (2021) montre mem sign-la dan lis zet pies ki bann zelev finn invante: vre aleatwar ena plis seri ki dimounn atann.
Enn liv zistwar kazino rakont enn zwer ki so nimero finn sorti sink fwa ansinn ek apel sa enn rekor. Komie sa rar lor enn rou eropeen? Ek komie fwa sa ti bizin arive kik part dan enn kazino ki ena 20 latab, sakenn tourn 40 fwa par er, lizour kouma lanwit?
Montre solision-la
Repons Enn nimero ki finn nome davans sink fwa ansinn: 1 lor 69 milion. Nimport ki nimero ki sorti kat fwa ankor apre so premie sorti: 1 lor 1.87 milion. Sa kazino-la tourn apepre 7 milion fwa par an, alor li ti bizin trouv enn seri sink trwa ouswa kat fwa par an.
Enn nimero ki finn nome sorti avek sans 1/37 sakenn tour, alor sink ansinn ena sans (1/37)⁵ = 1 lor 69,343,957. Me personn pa nom nimero-la davans. Nimport ki nimero sorti premie, kat tour swivan bizin repet li: (1/37)⁴ = 1 lor 1,874,161.
20 latab × 40 tour × 24 er × 365 zour = 7,008,000 tour par an. Sakenn tour kapav koumans enn seri, alor kazino-la atann 7,008,000/1,874,161 ≈ 3.7 seri sink par an.
Pena okenn rekor ofisiel kalite-la, ek nou pa bizin enn: enn evennman rar lor enn latab vinn enn zafer kouran lor enn kazino antie, ek bann zistwar rakont latab kot sa finn arive. Zistwar-la, dan Goldman (2007), pas lor enn rou doub zero, kot bann sif se 1 lor 79 milion ek 1 lor 2.09 milion.
Enpe riye
Long seri, samem figir aleatwar.
Sours
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.